Finite Group Databasebeta

?

← Prev (#14579943) Next (#14579945) →

C₄₁×#476 #14579944

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 57 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41)(42,43,45,47)(44,48,49,46)(50,51,53,56)(52,54,57,55);(42,44,45,49)(43,46,47,48);(51,54)(52,57)(55,56)

Conjugacy classes & character table

779 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 157);